To calculate the true position of polar coordinates, you convert the polar coordinates (r, θ) into Cartesian coordinates (x, y) using the formulas: ( x = r \cdot \cos(θ) ) and ( y = r \cdot \sin(θ) ). Here, ( r ) represents the radial distance from the origin, and ( θ ) is the angle measured from the positive x-axis in radians. This conversion provides the exact position in a Cartesian coordinate system.
Both coordinates are negative in this case.
True. You can choose any two distinct points on a line to calculate the slope. The slope is determined by the formula (m = \frac{y_2 - y_1}{x_2 - x_1}), where ((x_1, y_1)) and ((x_2, y_2)) are the coordinates of the two points. As long as the points are not the same, the slope will represent the line's steepness.
They have negative values
No it is not true
Substitute the coordinates of the point into the equation of the line. If the result is true, then the point is on the line.
False
True
False
Some of them but not all. For example, uniqueness. The rectangular coordinates (x, y) represent a different point if either x or y is changed. This is also true for polar coordinate (r, a) but only if r > 0. For r = 0 the coordinates represent the same point, whatever a is. Thus (x, y) has a 1-to-1 mapping onto the plane but the polar coordinates don't.
False
Square root of x + y divided by 2
True
Both coordinates are negative in this case.
Yes, it is true.
True
Their first coordinates are positive and their second coordinates are negative.
Polar Bears have black skin. Belive it or not, it's true.